We allow the pACP to deploy prediction models with the option to abstain, also known as selective prediction models [1]}.
We assume there is some known cost \(\delta > 0\)  for abstaining.
So, a selective prediction model incurs loss \(\ell \)  when it makes a prediction and \(\delta \)  when it abstains.
For notational convenience, define \(G_0\)  as a selective prediction model that always abstains.
In addition, define \(\ell _{\delta }(z, y)\)  to be the augmented loss function that is equal to \(\ell (z, y)\)  when \(z\)  is a prediction and \(\delta \)  when \(z\)  is the abstention option.
